Clustering+Python+Lab.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Overview**<br>\n",
    "<a href=\"https://archive.ics.uci.edu/ml/datasets/online+retail\">Online retail is a transnational data set</a> which contains all the transactions occurring between 01/12/2010 and 09/12/2011 for a UK-based and registered non-store online retail. The company mainly sells unique all-occasion gifts. Many customers of the company are wholesalers.\n",
    "\n",
    "The steps are broadly:\n",
    "1. Read and understand the data\n",
    "2. Clean the data\n",
    "3. Prepare the data for modelling\n",
    "4. Modelling\n",
    "5. Final analysis and reco"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Read and visualise the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import datetime as dt\n",
    "\n",
    "import sklearn\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_score\n",
    "\n",
    "from scipy.cluster.hierarchy import linkage\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from scipy.cluster.hierarchy import cut_tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "        InvoiceDate  UnitPrice  CustomerID         Country  \n",
       "0  01-12-2010 08:26       2.55     17850.0  United Kingdom  \n",
       "1  01-12-2010 08:26       3.39     17850.0  United Kingdom  \n",
       "2  01-12-2010 08:26       2.75     17850.0  United Kingdom  \n",
       "3  01-12-2010 08:26       3.39     17850.0  United Kingdom  \n",
       "4  01-12-2010 08:26       3.39     17850.0  United Kingdom  "
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read the dataset\n",
    "retail_df = pd.read_csv(\"Online_Retail.csv\", sep=\",\", encoding=\"ISO-8859-1\", header=0)\n",
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 541909 entries, 0 to 541908\n",
      "Data columns (total 8 columns):\n",
      "InvoiceNo      541909 non-null object\n",
      "StockCode      541909 non-null object\n",
      "Description    540455 non-null object\n",
      "Quantity       541909 non-null int64\n",
      "InvoiceDate    541909 non-null object\n",
      "UnitPrice      541909 non-null float64\n",
      "CustomerID     406829 non-null float64\n",
      "Country        541909 non-null object\n",
      "dtypes: float64(2), int64(1), object(5)\n",
      "memory usage: 33.1+ MB\n"
     ]
    }
   ],
   "source": [
    "# basics of the df\n",
    "retail_df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Clean the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InvoiceNo       0.00\n",
       "StockCode       0.00\n",
       "Description     0.27\n",
       "Quantity        0.00\n",
       "InvoiceDate     0.00\n",
       "UnitPrice       0.00\n",
       "CustomerID     24.93\n",
       "Country         0.00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 375,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# missing values\n",
    "round(100*(retail_df.isnull().sum())/len(retail_df), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(406829, 8)"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drop all rows having missing values\n",
    "retail_df = retail_df.dropna()\n",
    "retail_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
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       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "        InvoiceDate  UnitPrice  CustomerID         Country  \n",
       "0  01-12-2010 08:26       2.55     17850.0  United Kingdom  \n",
       "1  01-12-2010 08:26       3.39     17850.0  United Kingdom  \n",
       "2  01-12-2010 08:26       2.75     17850.0  United Kingdom  \n",
       "3  01-12-2010 08:26       3.39     17850.0  United Kingdom  \n",
       "4  01-12-2010 08:26       3.39     17850.0  United Kingdom  "
      ]
     },
     "execution_count": 377,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
       "      <th>amount</th>\n",
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       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>15.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>22.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "        InvoiceDate  UnitPrice  CustomerID         Country  amount  \n",
       "0  01-12-2010 08:26       2.55     17850.0  United Kingdom   15.30  \n",
       "1  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  \n",
       "2  01-12-2010 08:26       2.75     17850.0  United Kingdom   22.00  \n",
       "3  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  \n",
       "4  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  "
      ]
     },
     "execution_count": 378,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# new column: amount \n",
    "retail_df['amount'] = retail_df['Quantity']*retail_df['UnitPrice']\n",
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Prepare the data for modelling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- R (Recency): Number of days since last purchase\n",
    "- F (Frequency): Number of tracsactions\n",
    "- M (Monetary): Total amount of transactions (revenue contributed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
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      ],
      "text/plain": [
       "   CustomerID   amount\n",
       "0     12346.0     0.00\n",
       "1     12347.0  4310.00\n",
       "2     12348.0  1797.24\n",
       "3     12349.0  1757.55\n",
       "4     12350.0   334.40"
      ]
     },
     "execution_count": 379,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# monetary\n",
    "grouped_df = retail_df.groupby('CustomerID')['amount'].sum()\n",
    "grouped_df = grouped_df.reset_index()\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  frequency\n",
       "0     12346.0          2\n",
       "1     12347.0        182\n",
       "2     12348.0         31\n",
       "3     12349.0         73\n",
       "4     12350.0         17"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# frequency\n",
    "frequency = retail_df.groupby('CustomerID')['InvoiceNo'].count()\n",
    "frequency = frequency.reset_index()\n",
    "frequency.columns = ['CustomerID', 'frequency']\n",
    "frequency.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency\n",
       "0     12346.0     0.00          2\n",
       "1     12347.0  4310.00        182\n",
       "2     12348.0  1797.24         31\n",
       "3     12349.0  1757.55         73\n",
       "4     12350.0   334.40         17"
      ]
     },
     "execution_count": 381,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# merge the two dfs\n",
    "grouped_df = pd.merge(grouped_df, frequency, on='CustomerID', how='inner')\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
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       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>15.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>22.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>01-12-2010 08:26</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "        InvoiceDate  UnitPrice  CustomerID         Country  amount  \n",
       "0  01-12-2010 08:26       2.55     17850.0  United Kingdom   15.30  \n",
       "1  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  \n",
       "2  01-12-2010 08:26       2.75     17850.0  United Kingdom   22.00  \n",
       "3  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  \n",
       "4  01-12-2010 08:26       3.39     17850.0  United Kingdom   20.34  "
      ]
     },
     "execution_count": 382,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [],
   "source": [
    "# recency\n",
    "# convert to datetime\n",
    "retail_df['InvoiceDate'] = pd.to_datetime(retail_df['InvoiceDate'], \n",
    "                                          format='%d-%m-%Y %H:%M')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
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       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>15.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>22.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "          InvoiceDate  UnitPrice  CustomerID         Country  amount  \n",
       "0 2010-12-01 08:26:00       2.55     17850.0  United Kingdom   15.30  \n",
       "1 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34  \n",
       "2 2010-12-01 08:26:00       2.75     17850.0  United Kingdom   22.00  \n",
       "3 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34  \n",
       "4 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34  "
      ]
     },
     "execution_count": 384,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-12-09 12:50:00')"
      ]
     },
     "execution_count": 385,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the max date\n",
    "max_date = max(retail_df['InvoiceDate'])\n",
    "max_date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
       "      <th>amount</th>\n",
       "      <th>diff</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>536365</td>\n",
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       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>15.30</td>\n",
       "      <td>373 days 04:24:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "      <td>373 days 04:24:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
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       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
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       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>22.00</td>\n",
       "      <td>373 days 04:24:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "      <td>373 days 04:24:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>20.34</td>\n",
       "      <td>373 days 04:24:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "          InvoiceDate  UnitPrice  CustomerID         Country  amount  \\\n",
       "0 2010-12-01 08:26:00       2.55     17850.0  United Kingdom   15.30   \n",
       "1 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34   \n",
       "2 2010-12-01 08:26:00       2.75     17850.0  United Kingdom   22.00   \n",
       "3 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34   \n",
       "4 2010-12-01 08:26:00       3.39     17850.0  United Kingdom   20.34   \n",
       "\n",
       "               diff  \n",
       "0 373 days 04:24:00  \n",
       "1 373 days 04:24:00  \n",
       "2 373 days 04:24:00  \n",
       "3 373 days 04:24:00  \n",
       "4 373 days 04:24:00  "
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the diff\n",
    "retail_df['diff'] = max_date - retail_df['InvoiceDate']\n",
    "retail_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>CustomerID</th>\n",
       "      <th>diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>325 days 02:33:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>1 days 20:58:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>74 days 23:37:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>18 days 02:59:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>309 days 20:49:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID              diff\n",
       "0     12346.0 325 days 02:33:00\n",
       "1     12347.0   1 days 20:58:00\n",
       "2     12348.0  74 days 23:37:00\n",
       "3     12349.0  18 days 02:59:00\n",
       "4     12350.0 309 days 20:49:00"
      ]
     },
     "execution_count": 387,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# recency\n",
    "last_purchase = retail_df.groupby('CustomerID')['diff'].min()\n",
    "last_purchase = last_purchase.reset_index()\n",
    "last_purchase.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "      <td>325 days 02:33:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "      <td>1 days 20:58:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "      <td>74 days 23:37:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "      <td>18 days 02:59:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "      <td>309 days 20:49:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency           recency\n",
       "0     12346.0     0.00          2 325 days 02:33:00\n",
       "1     12347.0  4310.00        182   1 days 20:58:00\n",
       "2     12348.0  1797.24         31  74 days 23:37:00\n",
       "3     12349.0  1757.55         73  18 days 02:59:00\n",
       "4     12350.0   334.40         17 309 days 20:49:00"
      ]
     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# merge\n",
    "grouped_df = pd.merge(grouped_df, last_purchase, on='CustomerID', how='inner')\n",
    "grouped_df.columns = ['CustomerID', 'amount', 'frequency', 'recency']\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "      <td>325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "      <td>309</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency  recency\n",
       "0     12346.0     0.00          2      325\n",
       "1     12347.0  4310.00        182        1\n",
       "2     12348.0  1797.24         31       74\n",
       "3     12349.0  1757.55         73       18\n",
       "4     12350.0   334.40         17      309"
      ]
     },
     "execution_count": 389,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of days only\n",
    "grouped_df['recency'] = grouped_df['recency'].dt.days\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'whiskers': [<matplotlib.lines.Line2D at 0x1a3c2e6320>,\n",
       "  <matplotlib.lines.Line2D at 0x1a3c2e67b8>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x1a3c2e6be0>,\n",
       "  <matplotlib.lines.Line2D at 0x1a3c2e7048>],\n",
       " 'boxes': [<matplotlib.lines.Line2D at 0x1a3c2e61d0>],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x1a3c2e7470>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x1a3c2e7898>],\n",
       " 'means': []}"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bklyV5HeB24DdQ/ouSdI8hjJ1U1UvJfkQsBe4CLi/qg4N47skSfMb2m/dVNUeYM+wzi9J6o9PxkpS4wx6SWqcQS9JjTPoJalxBr0kNS7nw8MdSaaBH4+6D+ks1gA/G3UTUg9/UFULPnF6XgS9dD5LMlFV46PuQ1oqp24kqXEGvSQ1zqCXFrZj1A1Ig3COXpIa5xW9JDXOoJfOIsn9SU4keXLUvUiDMOils3sAuHHUTUiDMuils6iqbwLPjroPaVAGvSQ1zqCXpMYZ9JLUOINekhpn0EtnkWQX8F/AHyeZSnL7qHuSlsInYyWpcV7RS1LjDHpJapxBL0mNM+glqXEGvSQ1zqCXpMYZ9JLUOINekhr3/45FSiDcQicyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. outlier treatment\n",
    "plt.boxplot(grouped_df['recency'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [],
   "source": [
    "# two types of outliers:\n",
    "# - statistical\n",
    "# - domain specific"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [],
   "source": [
    "# removing (statistical) outliers\n",
    "Q1 = grouped_df.amount.quantile(0.05)\n",
    "Q3 = grouped_df.amount.quantile(0.95)\n",
    "IQR = Q3 - Q1\n",
    "grouped_df = grouped_df[(grouped_df.amount >= Q1 - 1.5*IQR) & (grouped_df.amount <= Q3 + 1.5*IQR)]\n",
    "\n",
    "# outlier treatment for recency\n",
    "Q1 = grouped_df.recency.quantile(0.05)\n",
    "Q3 = grouped_df.recency.quantile(0.95)\n",
    "IQR = Q3 - Q1\n",
    "grouped_df = grouped_df[(grouped_df.recency >= Q1 - 1.5*IQR) & (grouped_df.recency <= Q3 + 1.5*IQR)]\n",
    "\n",
    "# outlier treatment for frequency\n",
    "Q1 = grouped_df.frequency.quantile(0.05)\n",
    "Q3 = grouped_df.frequency.quantile(0.95)\n",
    "IQR = Q3 - Q1\n",
    "grouped_df = grouped_df[(grouped_df.frequency >= Q1 - 1.5*IQR) & (grouped_df.frequency <= Q3 + 1.5*IQR)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4293, 3)"
      ]
     },
     "execution_count": 393,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. rescaling\n",
    "rfm_df = grouped_df[['amount', 'frequency', 'recency']]\n",
    "\n",
    "# instantiate\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# fit_transform\n",
    "rfm_df_scaled = scaler.fit_transform(rfm_df)\n",
    "rfm_df_scaled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.723738</td>\n",
       "      <td>-0.752888</td>\n",
       "      <td>2.301611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.731617</td>\n",
       "      <td>1.042467</td>\n",
       "      <td>-0.906466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.300128</td>\n",
       "      <td>-0.463636</td>\n",
       "      <td>-0.183658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.277517</td>\n",
       "      <td>-0.044720</td>\n",
       "      <td>-0.738141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.533235</td>\n",
       "      <td>-0.603275</td>\n",
       "      <td>2.143188</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     amount  frequency   recency\n",
       "0 -0.723738  -0.752888  2.301611\n",
       "1  1.731617   1.042467 -0.906466\n",
       "2  0.300128  -0.463636 -0.183658\n",
       "3  0.277517  -0.044720 -0.738141\n",
       "4 -0.533235  -0.603275  2.143188"
      ]
     },
     "execution_count": 394,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfm_df_scaled = pd.DataFrame(rfm_df_scaled)\n",
    "rfm_df_scaled.columns = ['amount', 'frequency', 'recency']\n",
    "rfm_df_scaled.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Modelling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=50,\n",
       "    n_clusters=4, n_init=10, n_jobs=1, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 395,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# k-means with some arbitrary k\n",
    "kmeans = KMeans(n_clusters=4, max_iter=50)\n",
    "kmeans.fit(rfm_df_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 0, ..., 3, 0, 0], dtype=int32)"
      ]
     },
     "execution_count": 396,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [],
   "source": [
    "# help(KMeans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding the Optimal Number of Clusters\n",
    "\n",
    "### SSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a545bf400>]"
      ]
     },
     "execution_count": 398,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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u/BDSkhO0VLSIdBsFQIRKS07kxrPzee2TbayvrA+7HBHpgRQAEezmiYUkxsdpqWgR6RYKgAiWk9aLb43N47mSTfxuwRqaW3RaqIh0HQVAhLvnkpOZetpAfv3aZ1z/2Ltsrd0bdkki0kMoACJcWnIiv/3eaH597Zl8VF7L1AcW8doKXSUsIsdPARAFzIxvFw/h5Z9MIj8rhTv+cxn3zP2IPfubwi5NRKKYAiCKFGanMueOc7nz/GE8W7KJyx5czIrNtWGXJSJRSgEQZZIS4vj51JN56gcT2LO/mat+9zYzF66lRRPEItJBCoAode6wbF69exJfP7k///zKp3z/8ffZvmtf2GWJSBRRAESxjNQkHr5hLP9y9RmUbqhh6gMLmb9ye9hliUiUUABEOTPju+OH8ucfn8fg9N7c9mQJf//Cx7qtpIgckwKghxjevw/P//BcZkwu4qn3NnL5bxezcsuusMsSkQimAOhBeiXE83ffPIU/3DqeXXsbufI/3mbW4vWaIBaRw1IA9ECTRuTw6t2TmDwym/teWslNTyxlx25NEIvIododAGYWb2bLzeylYLvQzN4zs9Vm9qyZJQXtvYLtNcHrBW0+4xdB+2dmdnFX74x8IatPLx79fjH3XXk6762r4pIHFvHmp5ogFpEvdOQI4G5gVZvtfwX+3d1HADXArUH7rUCNuw8H/j3oh5mdClwHnAZMBX5nZvHHV74cjZlx49n5/PnH55GT1otbnijhl/M+YV+jJohFpJ0BYGZ5wKXAY8G2AV8H5gRdZgNXBs+nBdsEr18Q9J8GPOPuDe6+HlgDjO+KnZCjGzkgjT/dNZFbJhbyxDtlTPvt23y2bXfYZYlIyNp7BPAA8LdAS7CdBex09wOL0ZQDucHzXGATQPB6bdD/YPth3nOQmc0wsxIzK6moqOjArsjRJCfG8z8vP5Unbh5HVX0Dl/92MbPfKcNdE8QiseqYAWBmlwE73L20bfNhuvoxXjvae75ocJ/p7sXuXpyTk3Os8qSDzj+pP6/ePZmJw7K4d94n3Dq7hMq6hrDLEpEQtOcIYCJwhZmVAc/QOvTzAJBuZglBnzxgS/C8HBgCELzeD6hu236Y98gJlJPWi8dvGscvLz+VxWsqmfrAIt76XEdbIrHmmAHg7r9w9zx3L6B1EvdNd78e+CtwbdBtOvBi8HxesE3w+pveOs4wD7guOEuoEBgBvN9leyIdYmbcNLGQeT+aSGZqItMff5/7XlpJQ5MmiEVixfFcB/Bz4GdmtobWMf5ZQfssICto/xlwD4C7fwI8B6wEXgPucnf9tgnZyQP7Mu9H5zH9nHxmLV7Plf/xDqu3a4JYJBZYJE8CFhcXe0lJSdhlxIw3Vm3nb+Z8RH1DE/942alcP2EorSdwiUg0MbNSdy8+Vj9dCSwHXXDKAF776STGF2byD39awYw/lFJdvz/sskSkmygA5BD905KZffN4/uHSU3jrswqmPrCQt9dUhl2WiHQDBYB8RVyc8YNJRbxw17mkJSdww6z3+JdXVrG/qeXYbxaRqKEAkCM6bXA/XvrxJL43fiiPLFzH1Q+9zdqKurDLEpEuogCQo+qdFM//vuoMHrlxLOU1e7nswcU88/5GXUEs0gMoAKRdLj5tIK//dDJj8tO55/mP+eFTy9i5RxPEItFMASDtNqBvMn+4ZQK/uORk/nvVdi75zSKWrK0KuywR6SQFgHRIXJxx+5RhPH/nRHonxvO9x97l1699SmOzJohFoo0CQDrljLx+vPST8/hO8RB+t2At1z70DmWV9WGXJSIdoACQTktJSuD+a87koevHUFa1h0sfXMR/lWzSBLFIlFAAyHG75IxBvHr3JM7I68ffzPmIHz29nNq9jWGXJSLHoACQLjE4vTdP/eBs/ubik3h9xTa++ZtFvL++OuyyROQoFADSZeLjjLu+Npw5d55LQrxx3cwl/NtfPqNJE8QiEUkBIF1u1JB0Xv7JJK4ek8eDb67hW48sYWPVnrDLEpEvUQBIt+jTK4H/862z+H/fHc2aHXV888FFvLC8POyyRKQNBYB0q8vPGsyrd0/ilEFp/I9nP2T64+/z2oqtuvOYSATQDWHkhGhucWYuXMfv317Pjt0NpKckcsVZg7l2bB5n5PbTjWdEulB7bwijAJATqqm5hcVrKplTWs5fVm5nf1MLI/r34ZqxeVw1OpcBfZPDLlEk6ikAJOLV7m3k5Y+2MndZOaUbaogzmDQih2vG5nHRqQNITowPu0SRqKQAkKiyrqKO55dt5vll5Wyp3UdacgKXnTmYa8fmMmZohoaIRDpAASBRqaXFWbKuirml5by6Yht7G5spzE7l6tG5XD02j9z03mGXKBLxFAAS9eoamnjl463MLS3nvfXVmME5RVlcMyaPS84YSEpSQtglikQkBYD0KJuq9/D8ss3MXVbOxuo9pCbFc8kZg7hmTB4TCjOJi9MQkcgBCgDpkdydpWU1zC0t5+WPt1LX0EReRm+uHpPHNWNyyc9KDbtEkdB1WQCYWTKwEOgFJABz3P1eMysEngEygWXAje6+38x6AU8CY4Eq4DvuXhZ81i+AW4Fm4Cfu/vrRvlsBIEezd38zr3+yjbnLylm8phJ3GFeQwbVj8/jmGYNIS04Mu0SRUHRlABiQ6u51ZpYILAbuBn4GPO/uz5jZw8CH7v6Qmf0QONPd7zCz64Cr3P07ZnYq8DQwHhgM/Dcw0t2PeEmoAkDaa2vt3oNDROsq6klOjOPi0wZy7dg8zh2WTbyGiCSGdMsQkJml0BoAdwIvAwPdvcnMzgF+6e4Xm9nrwfMlZpYAbANygHsA3P1fgs862O9I36cAkI5ydz7YtJM5peX8+cMt7NrXxMC+yVw1JpdrxuQxvH+fsEsU6XbtDYB2nUZhZvFAKTAc+A9gLbDT3ZuCLuVAbvA8F9gEEIRDLZAVtL/b5mPbvkekS5gZo4dmMHpoBv942am8sWoHc5eVM3PhOh5asJZRQ9K5ZmweV5w5mH4pGiKS2NauAAiGaUaZWTrwAnDK4boFj4c71vajtB/CzGYAMwCGDh3anvJEDis5MZ5LzxzEpWcOYsfufby4fAtzl5Xzj39awX1/Xsk3Tu3PtWPzmDwih4R4rYsosadDJ1K7+04zWwCcDaSbWUJwFJAHbAm6lQNDgPJgCKgfUN2m/YC272n7HTOBmdA6BNShvRE5gv5pydw2uYgfTCrkky27mFNazrwPt/DKx9vI7tOLK0cN5pqxeZwyqG/YpYqcMO2ZBM4BGoNf/r2BvwD/CkwH5raZBP7I3X9nZncBZ7SZBL7a3b9tZqcBf+SLSeA3gBGaBJaw7G9q4a+f7WBuaTlvfrqDphbntMF9uWZMHtNGDSarT6+wSxTplK48C+hMYDYQT+v9A55z91+ZWRFfnAa6HLjB3RuC00b/AIym9S//69x9XfBZfw/cAjQBP3X3V4/23QoAOVGq6/cz74PNzFlWzorNu0iIM752cn+uGZPH10/uT1KChogkeuhCMJFO+mzbbuYuK+eF5Zup2N1ARkoi00a1nkV0em5fLUwnEU8BIHKcmppbWLS6kjnLypkf3Ltg5IA+XDOm9d4F/XXvAolQCgCRLlS7p5E/f9R6FtHyjTuJMxibn8GkETlMGpHNmXnputhMIoYCQKSbrK2o48Xlm1nweQUfb67FHfr1TmTi8Cwmj8hh0sgcLVstoVIAiJwA1fX7eXtNJQs/r2DR6kq27doHQFFOamsYjMjm7KIsUntp6Wo5cRQAIieYu7NmRx0LV1eyaHUF766rYl9jC4nxdnC4aPKIHE4b3FfLV0u3UgCIhGxfYzOlG2pYuLqCRZ9XsnLrLgAyU5M4b3g2k0ZkM2lEDgP7aTJZupYCQCTC7Ni9j7fXVLLo80oWrq6ksq4BgJED+hycOxhfkEnvpPiQK5VopwAQiWDuzqfbdh+cO3i/rJr9TS0kJcQxviCTSSOymTwyh5MHpum6A+kwBYBIFNm7v5n3y6pZFATCZ9t3A5CT1otJw7OZNDKb84bnkJOm5Snk2Lp0OWgR6V69k+KZMjKHKSNzANhWu49Fq1vDYMHnFTy/fDMApwzqy+SR2UwekcPY/AySEzVcJJ2nIwCRCNfS4nyyZVfrZPLqCko31NDY7CQnxjGhMIvJI3OYPCKb4f37aLhIAA0BifRY9Q1NvLe+ioWfV7JwdQXrKuoBGNg3+eDcwcTh2WSmJoVcqYRFASASI8pr9rB4dSWLVleyeE0ltXsbMYMzcvsdPNV0zNAMrWgaQxQAIjGoucX5qHwni4KL0ZZt3Elzi5OaFM85w7IOrl1UmJ2q4aIeTAEgIuza18iStVUHJ5Q3VO0BIDe998HJ5HOHZev+yD2MAkBEvmJDVT2LVreuXbRkbRW7G5qIMzh5YF/GFWRQXJDJ+MJMBmip66imABCRo2psbuHDTTtZvKaSkrIalm2sYc/+1ju0Dsnszbj8TMYVZjKuIINhOTrDKJroOgAROarE+DiKCzIpLsgEWgNh1dZdLC2rYen6ahau/uL6g4yURIoLWsNgXEEmpw3up0nlHkBHACJyWO7O+sp6SspqWFpWzdKyasqCOYTkxDhGDUlnfBAgY/Iz6KMlryOGhoBEpMvt2L3vYCCUlNXwyZZaWhziDE4d3Jfi/NY5hOKCDPqnaR4hLAoAEel2dQ1NLN9Yc3DYaPmmGvY1tgCQn5XCuDbDRjr19MTRHICIdLs+vRKCawta1zBqbG5hxebag0cJb366gzml5QBkpSZRHITBuIJMTh3cl8R4zSOESUcAItJt3J21FfUH5xBKymrYWN06j5CSFM/ooekHh41GDUnXrTO7iIaARCQibavdR8mG1jB4f301q7btwh3i44zTBvc9OGw0Nj9Ty193kgJARKLCrn2NLNtQc3DY6INNO2loap1HKMpOPWTYKD8rRfMI7dBlAWBmQ4AngYFACzDT3X9jZpnAs0ABUAZ8291rrPVf5zfAN4E9wE3uviz4rOnAPwQf/b/cffbRvlsBIBJ7GpqaWbF5VzBkVM3Sshpq9zYCrTfIGVeQQXF+ayCcMiiNBM0jfEVXBsAgYJC7LzOzNKAUuBK4Cah29/vN7B4gw91/bmbfBH5MawBMAH7j7hOCwCgBigEPPmesu9cc6bsVACLS0uKsqag7OIfw/vpqNu/cC0BqUjxj8oNAKMzgrDzNI0AXngXk7luBrcHz3Wa2CsgFpgHnB91mAwuAnwftT3prsrxrZulBiJwPzHf36qDA+cBU4OkO7ZmIxJS4OGPkgDRGDkjj+gn5AGzZufdgICwtq+aBNz7nwN+yA/r2oiArtfUnO5WCrJTgMZXeSbqDWlsdikozKwBGA+8BA4JwwN23mln/oFsusKnN28qDtiO1i4h0yOD03kwblcu0Ua2/Qmr3NLJsYw0rNtdSVrWHDVX1vPHpdirr9h/yviOFQ35WCilJsXfk0O49NrM+wFzgp+6+6ygTMYd7wY/S/uXvmQHMABg6dGh7yxORGNYvJZGvndyfr53c/5D23fsa2VC1h/WV9Wyoqmd95dHDIT8rlcIYCod27ZWZJdL6y/8pd38+aN5uZoOCv/4HATuC9nJgSJu35wFbgvbzv9S+4Mvf5e4zgZnQOgfQ7j0REfmStORETs/tx+m5/b7y2oFwKKuqp6yynrKqPZRV1vPGpzuorGs4pG/bcMjPTml9zEqlIDu6w+GYlQdn9cwCVrn7v7V5aR4wHbg/eHyxTfuPzOwZWieBa4OQeB34ZzPLCPpdBPyia3ZDRKRj2hsOB44gjhQO/dN6fWWuoSBKwqE91U0EbgQ+NrMPgra/o/UX/3NmdiuwEfhW8NortJ4BtIbW00BvBnD3ajO7D1ga9PvVgQlhEZFI0tFw2FBVz5ufVlBZV35I3yOFQ35WSkScraQLwUREukhdQxNllfVfGlpqHV6q2H2YI4fgSCE/K5XCYL6hICv1uMNBi8GJiJxgfXolHPHIoa6hiQ1V9ZRVHhoOf/2sgordhx455KT14spRg/n7S0/t1noVACIiJ0CfXgmcNrgfpw1uXzgM7Ne722tSAIiIhOxo4dCdtIiGiEiMUgCIiMQoBYCISIxSAIiIxCgFgIhIjFIAiIjEKAWAiEiMUgBbszTgAAADg0lEQVSIiMSoiF4LyMwqgA3H8RHZQGUXlROmnrIfoH2JRD1lP0D7ckC+u+ccq1NEB8DxMrOS9iyIFOl6yn6A9iUS9ZT9AO1LR2kISEQkRikARERiVE8PgJlhF9BFesp+gPYlEvWU/QDtS4f06DkAERE5sp5+BCAiIkfQIwPAzKaa2WdmtsbM7gm7ns4ys8fNbIeZrQi7luNlZkPM7K9mtsrMPjGzu8OuqTPMLNnM3jezD4P9+KewazpeZhZvZsvN7KWwazkeZlZmZh+b2QdmFrX3kjWzdDObY2afBv9fzum27+ppQ0BmFg98DlwIlNN6E/rvuvvKUAvrBDObDNQBT7r76WHXczzMbBAwyN2XmVkaUApcGW3/LmZmQKq715lZIrAYuNvd3w25tE4zs58BxUBfd78s7Ho6y8zKgGJ3j+rrAMxsNrDI3R8zsyQgxd13dsd39cQjgPHAGndf5+77gWeAaSHX1CnuvhCoDruOruDuW919WfB8N7AKyA23qo7zVnXBZmLwE7V/RZlZHnAp8FjYtQiYWV9gMjALwN33d9cvf+iZAZALbGqzXU4U/qLpycysABgNvBduJZ0TDJl8AOwA5rt7VO5H4AHgb4GWsAvpAg78xcxKzWxG2MV0UhFQAfw+GJZ7zMxSu+vLemIA2GHaovYvtJ7GzPoAc4GfuvuusOvpDHdvdvdRQB4w3syicnjOzC4Ddrh7adi1dJGJ7j4GuAS4KxhCjTYJwBjgIXcfDdQD3TaP2RMDoBwY0mY7D9gSUi3SRjBmPhd4yt2fD7ue4xUcmi8ApoZcSmdNBK4Ixs6fAb5uZv8Zbkmd5+5bgscdwAu0DgdHm3KgvM1R5RxaA6Fb9MQAWAqMMLPCYALlOmBeyDXFvGDydBawyt3/Lex6OsvMcswsPXjeG/gG8Gm4VXWOu//C3fPcvYDW/ydvuvsNIZfVKWaWGpxcQDBkchEQdWfPufs2YJOZnRQ0XQB024kSCd31wWFx9yYz+xHwOhAPPO7un4RcVqeY2dPA+UC2mZUD97r7rHCr6rSJwI3Ax8H4OcDfufsrIdbUGYOA2cHZZnHAc+4e1adP9hADgBda/84gAfiju78Wbkmd9mPgqeAP2HXAzd31RT3uNFAREWmfnjgEJCIi7aAAEBGJUQoAEZEYpQAQEYlRCgARkRilABARiVEKABGRGKUAEBGJUf8fA0mO3RKXgJYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# elbow-curve/SSD\n",
    "ssd = []\n",
    "range_n_clusters = [2, 3, 4, 5, 6, 7, 8]\n",
    "for num_clusters in range_n_clusters:\n",
    "    kmeans = KMeans(n_clusters=num_clusters, max_iter=50)\n",
    "    kmeans.fit(rfm_df_scaled)\n",
    "    \n",
    "    ssd.append(kmeans.inertia_)\n",
    "    \n",
    "# plot the SSDs for each n_clusters\n",
    "# ssd\n",
    "plt.plot(ssd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette Analysis\n",
    "\n",
    "$$\\text{silhouette score}=\\frac{p-q}{max(p,q)}$$\n",
    "\n",
    "$p$ is the mean distance to the points in the nearest cluster that the data point is not a part of\n",
    "\n",
    "$q$ is the mean intra-cluster distance to all the points in its own cluster.\n",
    "\n",
    "* The value of the silhouette score range lies between -1 to 1. \n",
    "\n",
    "* A score closer to 1 indicates that the data point is very similar to other data points in the cluster, \n",
    "\n",
    "* A score closer to -1 indicates that the data point is not similar to the data points in its cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For n_clusters=2, the silhouette score is 0.5415858652525395\n",
      "For n_clusters=3, the silhouette score is 0.5084896296141937\n",
      "For n_clusters=4, the silhouette score is 0.4814786837400834\n",
      "For n_clusters=5, the silhouette score is 0.4658529685822305\n",
      "For n_clusters=6, the silhouette score is 0.41707960376211345\n",
      "For n_clusters=7, the silhouette score is 0.4158077420309644\n",
      "For n_clusters=8, the silhouette score is 0.4059904161107271\n"
     ]
    }
   ],
   "source": [
    "# silhouette analysis\n",
    "range_n_clusters = [2, 3, 4, 5, 6, 7, 8]\n",
    "\n",
    "for num_clusters in range_n_clusters:\n",
    "    \n",
    "    # intialise kmeans\n",
    "    kmeans = KMeans(n_clusters=num_clusters, max_iter=50)\n",
    "    kmeans.fit(rfm_df_scaled)\n",
    "    \n",
    "    cluster_labels = kmeans.labels_\n",
    "    \n",
    "    # silhouette score\n",
    "    silhouette_avg = silhouette_score(rfm_df_scaled, cluster_labels)\n",
    "    print(\"For n_clusters={0}, the silhouette score is {1}\".format(num_clusters, silhouette_avg))\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=50,\n",
       "    n_clusters=3, n_init=10, n_jobs=1, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# final model with k=3\n",
    "kmeans = KMeans(n_clusters=3, max_iter=50)\n",
    "kmeans.fit(rfm_df_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 1, ..., 2, 1, 1], dtype=int32)"
      ]
     },
     "execution_count": 401,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>cluster_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "      <td>325</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "      <td>74</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "      <td>309</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency  recency  cluster_id\n",
       "0     12346.0     0.00          2      325           2\n",
       "1     12347.0  4310.00        182        1           0\n",
       "2     12348.0  1797.24         31       74           1\n",
       "3     12349.0  1757.55         73       18           1\n",
       "4     12350.0   334.40         17      309           2"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# assign the label\n",
    "grouped_df['cluster_id'] = kmeans.labels_\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a485086d8>"
      ]
     },
     "execution_count": 403,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "sns.boxplot(x='cluster_id', y='amount', data=grouped_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hierarchical Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.723738</td>\n",
       "      <td>-0.752888</td>\n",
       "      <td>2.301611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.731617</td>\n",
       "      <td>1.042467</td>\n",
       "      <td>-0.906466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.300128</td>\n",
       "      <td>-0.463636</td>\n",
       "      <td>-0.183658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.277517</td>\n",
       "      <td>-0.044720</td>\n",
       "      <td>-0.738141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.533235</td>\n",
       "      <td>-0.603275</td>\n",
       "      <td>2.143188</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     amount  frequency   recency\n",
       "0 -0.723738  -0.752888  2.301611\n",
       "1  1.731617   1.042467 -0.906466\n",
       "2  0.300128  -0.463636 -0.183658\n",
       "3  0.277517  -0.044720 -0.738141\n",
       "4 -0.533235  -0.603275  2.143188"
      ]
     },
     "execution_count": 406,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfm_df_scaled.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>cluster_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "      <td>325</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "      <td>74</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "      <td>309</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency  recency  cluster_id\n",
       "0     12346.0     0.00          2      325           2\n",
       "1     12347.0  4310.00        182        1           0\n",
       "2     12348.0  1797.24         31       74           1\n",
       "3     12349.0  1757.55         73       18           1\n",
       "4     12350.0   334.40         17      309           2"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# single linkage\n",
    "mergings = linkage(rfm_df_scaled, method=\"single\", metric='euclidean')\n",
    "dendrogram(mergings)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# complete linkage\n",
    "mergings = linkage(rfm_df_scaled, method=\"complete\", metric='euclidean')\n",
    "dendrogram(mergings)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0, ..., 0, 0, 0])"
      ]
     },
     "execution_count": 415,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 clusters\n",
    "cluster_labels = cut_tree(mergings, n_clusters=3).reshape(-1, )\n",
    "cluster_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>amount</th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>cluster_id</th>\n",
       "      <th>cluster_labels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12346.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "      <td>325</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12347.0</td>\n",
       "      <td>4310.00</td>\n",
       "      <td>182</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12348.0</td>\n",
       "      <td>1797.24</td>\n",
       "      <td>31</td>\n",
       "      <td>74</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12349.0</td>\n",
       "      <td>1757.55</td>\n",
       "      <td>73</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12350.0</td>\n",
       "      <td>334.40</td>\n",
       "      <td>17</td>\n",
       "      <td>309</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   amount  frequency  recency  cluster_id  cluster_labels\n",
       "0     12346.0     0.00          2      325           2               0\n",
       "1     12347.0  4310.00        182        1           0               1\n",
       "2     12348.0  1797.24         31       74           1               0\n",
       "3     12349.0  1757.55         73       18           1               0\n",
       "4     12350.0   334.40         17      309           2               0"
      ]
     },
     "execution_count": 416,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# assign cluster labels\n",
    "grouped_df['cluster_labels'] = cluster_labels\n",
    "grouped_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a5e154438>"
      ]
     },
     "execution_count": 419,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plots\n",
    "sns.boxplot(x='cluster_labels', y='recency', data=grouped_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a35360cc0>"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plots\n",
    "sns.boxplot(x='cluster_labels', y='frequency', data=grouped_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a48761320>"
      ]
     },
     "execution_count": 421,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plots\n",
    "sns.boxplot(x='cluster_labels', y='amount', data=grouped_df)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}